Title 
Implementation and evaluation of a splitting method for Total Variation deblurring 
Author

Lassen, Allan Lyngby

Supervisor

Hansen, Per Christian (Scientific Computing, Institut for Informatik og Matematisk Modellering, Danmarks Tekniske Universitet, DTU, DK2800 Kgs. Lyngby, Denmark)

Institution 
Technical University of Denmark, DTU, DK2800 Kgs. Lyngby, Denmark 
Thesis level 
Master's thesis 
Year 
2011 
Abstract 
This thesis takes basis in the solution to the inverse problem; the image deblurring
problem, and more specifically the Total Variation (TV) solution hereof. In
the field of research that is occupied with image deblurring, it is a well known
fact that this type of solution generally gives very visually pleasing results, but
at the cost of more complex computations. Some of the relevant theory behind
Inverse Problems will be covered, such as the Fredholm integral equation, and
an explanation of how this connects to the model for image deblurring.
Some introductory topics that leads to some of the simpler methods that solve
this problem, e.g. the 2norm Tikhonov solution and fast algorithms to decompose
structured matrices will be also covered in the introductory sections. Total
Variation and the computational issues that follows with the use of this type
of solution is described along with some of the actual implementations of how
these problems are treated through different algorithms.
Part of the thesis will be focused on the theory of the relatively new type of
solvers of the TV deblurring problem, the socalled splitting method. One specific method will be chosen for implementation, and the code for this method
will accordingly be implemented in Matlab and tested to see its computational
properties.
A number of Matlab methods, for which code is publicly available, will similarly
be analyzed in terms of their algorithmic specifications, and will be applied
to a set of chosen test problems as well as tested for their performance and usability
for the average user. Finally, the effect of the regularization parameters
will be analyzed with respect to noise, blur and image type. 
Imprint 
Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark 
Series 
IMMM.Sc.201112 
Fulltext 

Admin 
Creation date: 20110324
Update date: 20110324
Source: dtu
ID: 275691
Original MXD
